Nuclear magnetic resonance (NMR) measuring apparatuses and electron spin resonance (ESR) measuring apparatuses are conventionally known as representative magnetic resonance measuring apparatuses. Magnetic resonance imaging (MRI) apparatuses are known as devices similar to the NMR measuring apparatuses. Hereinafter, the ESR measuring apparatus will be described in detail below.
The ESR measuring apparatus is a type of magnetic resonance measuring apparatus, which can irradiate a sample placed in a static magnetic field with microwaves and record a state where the microwaves are absorbed by the sample as a spectrum.
Meanwhile, relaxation time of electron spin and nuclear spin, particularly spin lattice relaxation time (T1), corresponds to a parameter indicating physical properties and mobility of a magnetic material, or a parameter indicating oxygen concentration environment in which magnetic ions are placed in a living body. Measurement and evaluation of the relaxation time are important in fundamental research and applied research. Hereinafter, a method for measuring the T1 will be described.
First, a T1 measuring method that may be referred to as “inversion recovery method” will be described with reference to FIGS. 13 to 15. FIG. 13 illustrates an exemplary ESR measuring apparatus used for the measurement.
A sample tube, in which a sample 100 is placed, is disposed in a cavity 102 (e.g., a microwave resonator) functioning as a resonance circuit. The cavity 102 is disposed between two electromagnets 104, so that the cavity 102 can be placed in a static magnetic field generated by the electromagnets 104.
A microwave oscillator 106 generates microwaves and supplies the generated microwaves to a switch 108. The switch 108 performs a predetermined switching operation (e.g., ON and OFF switching operation) to form microwave pulses. An amplifier 110 amplifies the microwave pulses and supplies the amplified microwave pulses to the cavity 102 via a circulator 112.
When an ESR phenomenon occurs due to irradiation with the microwave pulses, reflected microwaves can be taken out via the circulator 112. The reflected microwaves are supplied to an amplifier 114. The reflected microwaves amplified by the amplifier 114 are supplied to a wave detector 116 (e.g., a mixer). A signal output from the wave detector 116 passes through an AD converter 118. Thus, a DC component signal is supplied to a personal computer (PC) 120. The PC 120 performs signal processing on the supplied signal to obtain an ESR spectrum signal.
FIG. 14 illustrates exemplary microwave pulses and spin echo intensity. The illustrated microwave pulses are exemplary microwave pulses that may be supplied in the measurement of the relaxation time T1 according to the inversion recovery method. The horizontal axis represents time.
The measurement of the relaxation time T1 includes irradiating the cavity 102 with a high-frequency high power pulse (i.e., π pulse) to invert the magnetization of the spin in the sample 100 with respect to the direction of the static magnetic field. The measurement further includes sequentially irradiating similar high-frequency high power pulses (i.e., π/2 pulse and π pulse) at the interval of time τ after a predetermined waiting time T elapses (Hahn echo sequence). In this case, the irradiation with the π/2 pulse may be performed only one time (FID sequence). A spin echo can be obtained when the Hahn echo sequence is performed. An FID signal can be obtained when the FID sequence is performed.
It is feasible to obtain spin echo intensity Iecho or peak intensity through FFT performed on the FID signal, corresponding to the waiting time T, by sequentially performing the measurements a plurality of times (e.g., 10 or more times) while changing the above-mentioned waiting time T.
FIG. 15 is a graph obtained by plotting the spin echo intensity Iecho with respect to the waiting time T. Fitting an exponential function defined by the following formula (1) to the obtained data of the spin echo intensity Iecho can obtain apparent relaxation time T1*.
                    [                  Numerical          ⁢                                          ⁢          expression          ⁢                                          ⁢          1                ]                                                                      I          echo                =                              I            0                    [                      (                          1              -                              2                ⁢                                  e                                      -                                          T                                              T                        1                        *                                                                                                                  )                    ]                                    (        1        )            
Next, a T1 measuring method that may be referred to as “saturation recovery method” will be described in detail below with reference to FIGS. 16 to 18. FIG. 16 illustrates an exemplary ESR measuring apparatus used for the measurement. The ESR measuring apparatus includes a path 122 provided to supply microwaves for monitoring, in addition to the configuration of the ESR measuring apparatus illustrated in FIG. 13. The rest of the configuration is similar to the configuration of the ESR measuring apparatus illustrated in FIG. 13.
FIG. 17 illustrates exemplary saturation pulse and detection signal (Imw). The saturation pulse is an example of the microwave pulse to be supplied in the measurement of the relaxation time T1 according to the saturation recovery method. The horizontal axis represents time.
The measurement of the relaxation time T1 includes irradiating the cavity 102 with a long-time high-frequency high power pulse (i.e., saturation pulse) and fixing the spin magnetization in the sample 100 to zero (0). The measurement further includes irradiating the cavity 102 with a high-frequency low power pulse upon terminating the irradiation with the high-frequency high power pulse (i.e., the saturation pulse), and sequentially monitoring recovery (or restoration) of the spin magnetization from the zero (0) fixed state to an equilibrium magnetization (detection signal Imw).
FIG. 18 is a graph obtained by plotting the detection signal Imw with respect to the time T. Fitting an exponential function defined by the following formula (2) to the obtained data of the detection signal Imw can obtain apparent relaxation time T1*.
                    [                  Numerical          ⁢                                          ⁢          expression          ⁢                                          ⁢          2                ]                                                                      I          mw                =                              I            0                    [                      (                          1              -                              2                ⁢                                  e                                      -                                          T                                              T                        1                        *                                                                                                                  )                    ]                                    (        2        )            
Next, a T1 measuring method that may be referred to as “frequency swept longitudinal detection method” (fs-LOD method) will be described in detail below with reference to FIGS. 19 to 21. FIG. 19 illustrates an exemplary ESR measuring apparatus used for the measurement.
A sample tube, in which a sample 100 is placed, is disposed in a cavity 102 that functions as a resonance circuit. The cavity 102 is disposed between two electromagnets 104. Further, pickup coils 124, each having a winding axis extending in a direction parallel to a static magnetic field, are disposed adjacently to the sample 100.
A microwave oscillator 106 generates microwaves and supplies the generated microwaves to a switch 108. On the other hand, a pulse generator 126 generates a reference signal with modulation frequency. The reference signal is supplied to the switch 108 so that the switch 108 can repeat ON and OFF operations according to the modulation frequency. In other words, the microwaves are modulated according to the modulation frequency. An amplifier 110 amplifies the modulated microwaves and supplies the amplified modulated microwaves to the cavity 102 via a circulator 112. When an ESR phenomenon occurs due to sweeping of the static magnetic field, an Mz component of the electron spin changes and induced voltage is generated in the pickup coils 124. An amplifier 114 amplifies the induced voltage and supplies the amplified voltage to a phase detector 128. Variation of the induced voltage is synchronous with the modulation frequency. Accordingly, the phase detector 128 performs lock-in detection using the reference signal supplied from a pulse generator 126. A signal output from the phase detector 128 passes through an AD converter 118. Thus, a DC component signal is supplied to a PC 120. The PC 120 performs signal processing on the supplied signal to obtain an ESR spectrum signal.
FIG. 20 illustrates modulation frequency and an example of lock-in detected signal. The modulation frequency is an example of the modulation frequency to be used in the measurement of the relaxation time T1 according to the frequency swept longitudinal detection method (fs-LOD method). The horizontal axis represents time.
The measurement of the relaxation time T1 includes causing the pulse generator 126 to modulate the output intensity of microwaves supplied from the microwave oscillator 106 at a predetermined modulation frequency fmod and irradiating the cavity 102 with the modulated microwaves. Similar effects can be obtained by performing simultaneous and continuous irradiation with two high-frequency components separated at frequency Δf corresponding to the modulation frequency fmod, instead of modulating the microwaves at the modulation frequency fmod.
The measurement further includes detecting temporal variation in magnetization of the spin in the direction of the static magnetic field, with the pickup coils 124, and performing the lock-in detection at the modulation frequency fmod or the frequency Δf, caused by the above-mentioned irradiation of the microwaves, so that a signal SLOD can be obtained.
Obtaining the signal SLOD while changing the modulation frequency fmod or the frequency Δf can obtain attenuation data of the signal SLOD depending on the modulation frequency. FIG. 21 is a graph illustrating the signal SLOD with respect to the modulation frequency. Fitting a function defined by the following formula (3) to the obtained data of the signal SLOD can obtain apparent relaxation time T1*.
                    [                  Numerical          ⁢                                          ⁢          expression          ⁢                                          ⁢          3                ]                                                                      S          LOD                =                  C                                                    1                                  T                  1                                      *                    2                                                              +                              ω                2                                                                        (        3        )            
Next, a T1 measuring method that may be referred to as the “perturbative LOT-T1 method” (p-LOD-T1 method) will be described with reference to FIGS. 22 to 24. FIG. 22 illustrates an exemplary ESR measuring apparatus for the measurement. The illustrated ESR measuring apparatus has a configuration basically similar to that of the ESR measuring apparatus illustrated in FIG. 19.
FIG. 23 illustrates a sequence of microwave pulses and examples of lock-in detected signals. The illustrated microwave pulses are microwave pulses that can be used in the measurement of the relaxation time T1 according to the perturbative LOT-T1 method (i.e., the p-LOD-T1 method).
The measurement of the relaxation time T1 includes causing a pulse generator 130 to continuously generate two pulse voltages at the interval of time τ every repetition time Trep, for modulation of the output intensity of the microwaves supplied from the microwave oscillator 106, and irradiating the cavity 102 with the modulated microwaves.
The measurement further includes detecting temporal variation in magnetization of the spin in the direction of the static magnetic field occurring due to the above-mentioned irradiation with microwaves, with the pickup coils 124, while changing the time τ and performing lock-in detection at a modulation frequency fmod=1/Trep so that the signal SLOD can be obtained. FIG. 24 is a graph illustrating the signal SLOD with respect to the time τ. In FIGS. 23 and 24, a curve indicated by reference numeral 132 illustrates the signal SLOD detected according to the perturbative LOT-T1 method (i.e., the p-LOD-T1 method) and a curve indicated by reference numeral 134 illustrates the signal SLOD detected according to the inversion LOD-T1 method. The microwave pulses with which the cavity 102 is irradiated according to the inversion LOD-T1 method are stronger than those according to the perturbative LOT-T1 method (i.e., the p-LOD-T1 method).
Fitting a function defined by the following formula (4) to the data of the signal SLOD detected according to the inversion LOD-T1 method can obtain the apparent relaxation time T1*.
                    [                  Numerical          ⁢                                          ⁢          expression          ⁢                                          ⁢          4                ]                                                                      S          LOD                =                              M            [                          1              -                              2                ⁢                                  e                                                            -                      τ                                                              T                      1                      *                                                                                            ]                    +                      K            ⁢                                          2                ⁢                                  (                                      1                    +                                          cos                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            mod                                                    ⁢                          τ                                                )                                                                              )                                                                                        (        4        )            
Further, fitting a function defined by the following formula (5) to the data of the signal SLOD detected according to the perturbative LOT-T1 method (i.e., the p-LOD-T1 method) can obtain the apparent relaxation time T1*.
                    [                  Numerical          ⁢                                          ⁢          expression          ⁢                                          ⁢          5                ]                                                                      S          LOD                =                              M            [                          e                                                -                  τ                                                  T                  1                  *                                                      ]                    +                      K            ⁢                                          2                ⁢                                  (                                      1                    +                                          cos                      ⁡                                              (                                                  2                          ⁢                          π                          ⁢                                                                                                          ⁢                                                      f                            mod                                                    ⁢                          τ                                                )                                                                              )                                                                                        (        5        )            
An apparatus discussed in Japanese Patent Application Laid-Open No. 2016-75665 is available in the measurement of the relaxation time according to the perturbative LOT-T1 method (i.e., the p-LOD-T1 method).
In the ESR measuring method and the NMR measuring method, a strong interaction different from the magnetic resonance is manifested between the spin and the resonance circuit (i.e., the cavity or the NMR probe), which may be called “spin-cavity coupling,” when the spin concentration (i.e., sample amount) of a sample is large, when the sample is a substance having strong magnetism, when the Q value of a cavity (resonator) or an NMR probe serving as a resonance circuit is very high, or when the spin lattice relaxation time is very long.
The spin-cavity coupling is a phenomenon constantly occurring when the resonance frequency of the spin coincides with the resonance frequency of the resonance circuit. However, if the spin concentration is low and the total amount of spin itself is very small, the coupling constant is so small that the measurement will not be hindered.
However, if the measurement is performed under the above-mentioned conditions, the following problems may arise. For example, the line width of a spectrum will become extraordinarily wider and the original spectrum of the substance will not appear. The spectrum will be distorted and the measurement itself will become unfeasible. During the measurement of the spin lattice relaxation time T1, spin-cavity coupling constant g(ω) will change to accelerate the relaxation, and obtaining a normal function will not be feasible. If the spin lattice relaxation time T1 of a magnetic substance is evaluated under such conditions, the observed apparent relaxation time T1* may be observed to be smaller than the substance's relaxation time T1 (i.e., true relaxation time T1), because the apparent line width is widened in the spectrum.
Due to the presence of the spin-cavity coupling, the observed relaxation time (i.e., the apparent relaxation time) will change depending on the amount of a sample placed in the resonance circuit (i.e., the cavity or the NMR probe), the Q value of the resonance circuit, or a sample filling rate for the resonance circuit. More specifically, even when the same sample is used, the obtained value of the relaxation time will vary depending on the specification of the detection circuit or the measuring method of the relaxation time T1. As mentioned above, it is difficult to accurately measure the relaxation time T1 when the spin concentration of a sample is high, when the Q value of the resonance circuit is extraordinarily high, or when the sample filling rate is very high.
The present disclosure intends to obtain an accurate relaxation time of a sample even under conditions where the influence of the spin-cavity coupling is large.